Atomic orbitals: 4d wave function

Schematic plot of the 4dz2 wave function ψ4dz2. The blue zones are where the wave function has negative values and the red zones denote positive values.

The graph on the left is a plot of values along a single line drawn through the nucleus along the z-axis, while the surface plot on the right shows values of ψ4dxy on a slice in the xz plane drawn through the nucleus.

In general, apart from the two nodal planes, d-orbitals have a number of radial nodes that separate the largest, outer, component from the inner components. The number of radial nodes is related to the principal quantum number, n. In general, a nd orbital has (n - 3) radial nodes, so 4d-orbitals have (4 - 3) = 1 radial node.

The equations for the 4d orbitals (ψ4d) show that in addition to a radial dependency, there is a dependency upon direction. This is why d orbitals are not spherical. This behaviour is unlike that of the s orbitals for which the value of the wave function for a given value of r is the same no matter what direction is chosen.